Aircraft: C172
Phase of flight: Other Maneuvers
Anomaly: Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural FAR

I am a seven year flight instructor. I was on a dual training flight in VFR conditions with an end of course student trying to obtain his private pilot license in a Cessna 172s-navIII with ADS-B. We had been flying for about an hour in Cottonwood practice area out by Cottonwood airport. I had my student put on the hood so that I could evaluate his Basic Attitude Instrument Flying. We were about 7 NM north of P52. I was simulating ATC to assess his turns to headings; climbs; level flight; and changes of airspeeds. I noticed a target on the ADS-B screen about 8 NM west from us and 500 FT lower in altitude heading towards Mingus Mountain and away from us. The target was about 3 NM southeast of Cottonwood airport. I made a new position report over the local practice area frequency and was monitoring the CTAF/Unicom for Cottonwood (P52). I regularly monitor Cottonwood airport's frequency in that area due to the high amount of sky diving activity into that airport. I was about to give my student some unusual attitudes that he could recover from. I noticed the target began moving towards us and it had climbed to our same altitude (8;000 FT MSL). I saw it about 6 NM away and appeared to be a helicopter. I started giving my student vectors to get out of its way; turned the tail of our plane towards the helicopter and began flying northwest. The target followed us. I lost sight of it; but it was still on our ADS-B. I continued giving my student changes in course to get away from it; but it stayed directly on our tail at the same altitude. It continued to close in on us until the ADS-B said that there was no distance between us. The helicopter appeared to be following us around on purpose trying to stay out of our sight. My student and I became very uneasy and I feared for our safety. It seemed as if this helicopter was practicing targeting us or seeing how close it could fly to us without being noticed. I had student pull up his hood. We discontinued maneuvers. I took controls added full power; began to climb and entered a steep bank turn to the left in an attempt to see where the target was. When we saw the helicopter; it was 100 FT horizontal and 200 FT vertical lower only because I had entered a climb. This happened [during mid-morning] off the 070 degree radial from DRK VOR 27 NM out. It appeared to my student and I that this helicopter realized after my evasive maneuver that we knew that he was following us. The helicopter flew slowly directly under us; stopped following us and began heading towards Sedona airport. My student and I were pretty shaken up and decided to discontinue flight and head towards Prescott airport.The helicopter was large; not a training aircraft. It was completely black. We did not notice any distinct tail number. I am not sure what kind of helicopter it was. It had two large vertical fins sticking out from where the tail rotor would be. We were unsure if this helicopter had blades on the tail rotor. We looked at pictures online and think that it was either an EC145 or an MD Explorer. I am not sure what I could have done differently. I considered calling Albuquerque Center and asking for assistance. I know that what this helicopter did was illegal as we had no prior knowledge or intention of formation flying on this flight and I did fear for my life. Maybe an alert area can be placed on the VFR sectional chart around Prescott warning pilots of concentrated student training in the area. I am unsure if I am supposed to report this incident to Phoenix FSDO as we were on local practice area frequency; not ATC and performing maneuvers not on any flight plan. A Cessna instructor with his student took evasive action from a helicopter which was apparently flying intentionally close in Class E Airspace about 27 miles east of DRK.